My apologies. This shows that x_1 approaches the expected value 49.50 as I reduce the tolerance. The differential state still remains outside of tolerance, however.
1e-8:
u = [49.479690908110484, 13.682966651643868, 0.5, 49.99999999999998]
1e-9:
u = [49.4915514356334, 13.685537303140494, 0.5, 49.99999999999999]
1e-10:
u = [49.494069541722695, 13.686082918800729, 0.5, 49.99999999999998]
1e-11:
u = [49.49822477214678, 13.686983072701429, 0.5, 49.999999999999986]
1e-12:
u = [49.49990766890697, 13.687347610721506, 0.5, 49.99999999999997]
I saw Yingbo’s BDF method derivation reference in his blog. Do you recommend any references for understanding of algebraic state interpolation?